In this case, the plumb-line is attached to one of the pillars which support the microscopes in the way above described ; and it has no reference to any fixed points or divisions on the limb of the circle, but only insures a si milarity of position in the index for each position of the instrument ; and provided that the plumb-line apparatus was free from all danger of derangement, this would be sufficient. This verification may perhaps be rendered more intelligible, by considering that a circular instru ment, in whatever manner its vertical axis be placed, in dicates, by a double observation, the angle which the ob ject makes with the axis, round which the whole instru ment has I evolved in passing from one position to the other. For let Pp be the axis, T x the telescope in one position ; it is evident that in turning the instrument half round, t y will then be the position of the tele scope, P x being equal to P y. The arc x y which the telescope passes through to regain its former position, is the quan tity really given by the instrument ; and if the axis Pp be vertical, half this quantity is the true zenith distance of the object. Now the intention of Mr Troughton's verification is to ensure a vertical position to the axis For instruments which rest on move-abli pillars, and turn freely in azimuth, this method is much to be pre ferred ; but it is not without a considerable defect, for it' by any derangement in the plumb-line apparatus, the error in collimation be changed, it cannot be restored with certainty to its former position, so that sometimes a very valuable series of observations may be lost, for want of a corresponding one to compare with it.
It was in 1792, after having made several smaller ones, that Troughton constructed a circle for Count Bruhl. The observations made with this instrument Were very few, but exceeded in accuracy any that had been made before. The diameter of this circle was only two feet, but we ate strongly inclined to believe that it exceeded in accuracy the five feet circle of Piazzi.
The equatorial instrument constructed by Ramsdell for Sir George Shuckburg, properly belongs to the class of astronomical circles. It will be more fully noticed under the article OBSERVATORY. Few observations have been, we believe, ever made with it. Indeed it is a waste of so very capital an instrument to place it in the equatorial position, because meridian observations will always ceteris paribus he better ; and in practical astro nomy, a second best method is absolutely of no u se. This valuable and superb instrument has lately been presented to the Royal Observatory of Greenwich by the Hon. Mr Jenkinson, and is intended to be used both in the vertical and inclined position ; and as an altitude and azimuth instrument, there can be no doubt but it will prove a most valuable acquisition.
An equatorial instrument by Troughton, of which the vertical circle was feet in diameter, was erected at Armagh ; and Dr Hamilton's observations made with it were inserted with Mr Pond's, in the Transactions of 1806.
Several other circles were made by Troughton of dif ferent dimensions, varying considerably in the subordi nate contrivances, but much resembling each other in their general principle. Mr Wollaston describes a very perfect instrument, by Troughton, of this kind, (not very unlike the one hereafter treated of,) in the Appen dix to his Fascieulus; and gives some excellent directions to less experienced observers, which we shall avail our selves of before we conclude this subject.
Mr Pond's catalogue of stars, which first demonstra ted the defect of the Greenwich quadrant, was deduced from observations made with a circle constructed by Troughton, 30 inches in diameter, and is minutely de scribed in the Philosophical Transactions. It is exactly similar to a smaller oae now possessed by General Bris bane, and of which we have given a representation in Plate XLVI. and a description in the article ASTRONOMY, VOL ii p. 682.
One of the most perfect instruments of the kind is that in the possession of Stephen Groombridge, Esq. of Blackheath. It is a transit circle placed between two piers, made according to the idea suggested by Mr Wollaston. The four microscopes are placed in the horizontal dia meter, two on each side, the instrument being on both sides divided. From observations made with tl.is instru ment, a very valuable paper on astronomical refractions has been already communicated to the public.
The largest astronomical circle that has been yet con structed, is that belonging to the observatory of Dublin.
The vertical circle is eight feet diameter. It was begun by Ramsdell, and finished by his successor Mr Berge. It was erected about the year 1807. We have not seen any printed description of it, nor have many observations made with been published ; but we understand that the learned astronomer, Dr Brinkley, to whose care it is now entrusted, is perfectly satisfied with its performance; and it is with this instrument that he has been able to in fer the apparent annual parallax of Lyre, which he esti mates to be between two or three seconds.
To the above, we may add a very beautiful two feet circle, in the possession likewise of General Brisbane, and which was actually the model of the six feet mural circle erected last summer at Greenwich. It differs in principle from all those above mentioned; and though it is not in our power at present to describe very minutely the mechanism of either of these instruments, of which no account has yet been published, we are nevertheless enabled to explain some of the more striking peculiari ties in their construction.